Enriched physics-informed neural networks for in-plane crack problems: Theory and MATLAB codes

TL;DR

This paper introduces an enriched physics-informed neural network (PINN) approach for modeling in-plane crack problems in linear elastic fracture mechanics, effectively capturing singular stress fields without complex meshing.

Contribution

The study develops a novel enriched PINN method that incorporates crack-tip asymptotic functions, simplifying the modeling of singularities compared to traditional FEM or BEM methods.

Findings

Accurately computes stress intensity factors with fewer degrees of freedom.

Enriched PINNs outperform standard PINNs in modeling crack-tip singularities.

Provides MATLAB codes for practical implementation.

Abstract

In this paper, a method based on the physics-informed neural networks (PINNs) is presented to model in-plane crack problems in the linear elastic fracture mechanics. Instead of forming a mesh, the PINNs is meshless and can be trained on batches of randomly sampled collocation points. In order to capture the theoretical singular behavior of the near-tip stress and strain fields, the standard PINNs formulation is enriched here by including the crack-tip asymptotic functions such that the singular solutions at the crack-tip region can be modeled accurately without a high degree of nodal refinement. The learnable parameters of the enriched PINNs are trained to satisfy the governing equations of the cracked body and the corresponding boundary conditions. It was found that the incorporation of the crack-tip enrichment functions in PINNs is substantially simpler and more trouble-free than in the finite element (FEM) or boundary element (BEM) methods. The present algorithm is tested on a class of representative benchmarks with different modes of loading types. Results show that the present method allows the calculation of accurate stress intensity factors (SIFs) with far fewer degrees of freedom. A self-contained MATLAB code and data-sets accompanying this manuscript are also provided.